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Keywords = graphyne

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36 pages, 7184 KiB  
Review
Exploration of Sp-Sp2 Carbon Networks: Advances in Graphyne Research and Its Role in Next-Generation Technologies
by Muhammad Danish Ali, Anna Starczewska, Tushar Kanti Das and Marcin Jesionek
Int. J. Mol. Sci. 2025, 26(11), 5140; https://doi.org/10.3390/ijms26115140 - 27 May 2025
Cited by 1 | Viewed by 452
Abstract
Graphyne, a hypothetical carbon allotrope comprising sp and sp2 hybridized carbon atoms, has garnered significant attention for its potential applications in next-generation technologies. Unlike graphene, graphyne’s distinctive acetylenic linkages endow it with a tunable electronic structure, directional charge transport, and superior mechanical [...] Read more.
Graphyne, a hypothetical carbon allotrope comprising sp and sp2 hybridized carbon atoms, has garnered significant attention for its potential applications in next-generation technologies. Unlike graphene, graphyne’s distinctive acetylenic linkages endow it with a tunable electronic structure, directional charge transport, and superior mechanical flexibility. This review delves into the structural variety, theoretical underpinnings, and burgeoning experimental endeavors associated with various graphyne allotropes, including α-, β-, γ-, and 6,6,12-graphyne. It examines synthesis methods, structural and electronic characteristics, and the material’s prospective roles in diverse fields, such as nanoelectronics, transistors, hydrogen storage, and desalination. Additionally, it highlights the use of computational modeling techniques—density functional theory (DFT), GW approximation, and nonequilibrium Green’s function (NEGF)—to anticipate and validate properties without fully scalable experimental data. Despite substantial theoretical progress, the practical implementation of graphyne-based devices faces several challenges. By critically assessing current research and identifying strategic directions, this review underscores graphyne’s potential to revolutionize advanced materials science. Full article
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13 pages, 6465 KiB  
Article
Prediction of Thermal Transport Properties of Pristine and BN-Substituted Holey Graphynes
by Qingchen Li, Yujie Zhang, Yanlong Liu, Yan Gao and Baoxia Deng
Inorganics 2025, 13(4), 128; https://doi.org/10.3390/inorganics13040128 - 21 Apr 2025
Viewed by 466
Abstract
The merging of pore designs is a potential strategy for achieving ultra-low lattice thermal conductivity (κ), for which phonon anharmonicity and size effect are indispensable for discovering novel functional materials in thermal applications. In this study, monolayer holey graphyne (HGY) and [...] Read more.
The merging of pore designs is a potential strategy for achieving ultra-low lattice thermal conductivity (κ), for which phonon anharmonicity and size effect are indispensable for discovering novel functional materials in thermal applications. In this study, monolayer holey graphyne (HGY) and boron nitride holey graphyne (BN-HGY) were examined for their phonon thermal transport properties through first-principles calculation and phonon Boltzmann function. HGY exhibits an intrinsic lattice thermal conductivity (κ) of 38.01 W/mK at room temperature, which exceeds BN-HGY’s 24.30 W/mK but is much lower than 3550 W/mK for BTE graphene. The phonon–phonon scattering behavior of BN-HGY is obviously increased compared to HGY due to the enhancement of anharmonicity, which leads to a shorter phonon lifetime and lower κ. Additionally, at room temperature, the representative mean free path (rMFP) of BN-HGY is substantially higher than that of HGY, and the κ of BN-HGY decreases faster at a larger rMFP (within a unit nm). This work will be constructive to further the application of HGY and BN-HGY as thermal management materials. Full article
(This article belongs to the Special Issue Boron-Based Low-Dimensional Nanoclusters and Nanomaterials)
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14 pages, 6961 KiB  
Article
Determine the Relative Aromaticity of Bilayer Graphyne, Bilayer Graphdiyne, and Bilayer Graphtriyne
by Gang Zhang, Xinwen Gai, Lulu Sun and Ji Ma
Molecules 2025, 30(2), 365; https://doi.org/10.3390/molecules30020365 - 17 Jan 2025
Viewed by 835
Abstract
The electronic structure characteristics of bilayer graphyne, bilayer graphdiyne, and bilayer graphtriyne were systematically studied using molecular orbital (MO) analysis, density of states (DOS), and interaction region indicator (IRI) methods. The delocalization characteristics of the out-of-plane and in-plane π electrons (i.e., πout [...] Read more.
The electronic structure characteristics of bilayer graphyne, bilayer graphdiyne, and bilayer graphtriyne were systematically studied using molecular orbital (MO) analysis, density of states (DOS), and interaction region indicator (IRI) methods. The delocalization characteristics of the out-of-plane and in-plane π electrons (i.e., πout and πin electrons) of these materials were analyzed using the localized orbital locator (LOL). In addition, their responses to external magnetic fields were investigated through anisotropic induced current density (AICD) and isoscalar chemical shielding surfaces (ICSSs) to compare the induced ring currents and magnetic shielding effects, further exploring the aromaticity of the three bilayer materials. The research results indicate that as the number of alkyne groups increases, the aromaticity of the bilayer graphyne structure gradually weakens. Finally, their photophysical properties were studied through TD-DFT calculations. The results show that they exhibit strong localized excitation characteristics. Full article
(This article belongs to the Section Materials Chemistry)
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15 pages, 10197 KiB  
Article
Effect of Strain Rate, Temperature, Vacancy, and Microcracks on Mechanical Properties of 8-16-4 Graphyne
by Qing Peng, Zeyu Huang, Gen Chen, Yuqiang Zhang, Xiaofan Zhang, Xiao-Jia Chen and Zhongwei Hu
Nanomaterials 2024, 14(6), 556; https://doi.org/10.3390/nano14060556 - 21 Mar 2024
Cited by 9 | Viewed by 2291
Abstract
The 8-16-4 graphyne, a recently identified two-dimensional carbon allotrope, exhibits distinctive mechanical and electrical properties, making it a candidate material for flexible electronic applications. This study endeavors to enhance our comprehension of the fracture behavior and mechanical properties of 8-16-4 graphyne. The mechanical [...] Read more.
The 8-16-4 graphyne, a recently identified two-dimensional carbon allotrope, exhibits distinctive mechanical and electrical properties, making it a candidate material for flexible electronic applications. This study endeavors to enhance our comprehension of the fracture behavior and mechanical properties of 8-16-4 graphyne. The mechanical properties of 8-16-4 graphyne were evaluated through molecular dynamics simulations, examining the impact of boundary conditions, temperature, and strain rate, as well as the coupled interactions between temperature, vacancy defects, and microcracks. The findings reveal that 8-16-4 graphyne undergoes fracture via the cleavage of ethylene bonds at a critical strain value of approximately 0.29. Variations in boundary conditions and strain rate influence the fidelity of tensile simulation outcomes. Temperature, vacancy concentration, and the presence of microcracks markedly affect the mechanical properties of 8-16-4 graphyne. In contrast to other carbon allotropes, 8-16-4 graphyne exhibits a diminished sensitivity to vacancy defects in its mechanical performance. However, carbon vacancies at particular sites are more prone to initiating cracks. Furthermore, pre-existing microcracks within the material can potentially alter the fracture mode. Full article
(This article belongs to the Section 2D and Carbon Nanomaterials)
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8 pages, 17726 KiB  
Communication
Electronic, Thermal and Mechanical Properties of Carbon and Boron Nitride Holey Graphyne Monolayers
by Bohayra Mortazavi
Materials 2023, 16(20), 6642; https://doi.org/10.3390/ma16206642 - 11 Oct 2023
Cited by 17 | Viewed by 2053
Abstract
In a recent experimental accomplishment, a two-dimensional holey graphyne semiconducting nanosheet with unusual annulative π-extension has been fabricated. Motivated by the aforementioned advance, herein we theoretically explore the electronic, dynamical stability, thermal and mechanical properties of carbon (C) and boron nitride (BN) holey [...] Read more.
In a recent experimental accomplishment, a two-dimensional holey graphyne semiconducting nanosheet with unusual annulative π-extension has been fabricated. Motivated by the aforementioned advance, herein we theoretically explore the electronic, dynamical stability, thermal and mechanical properties of carbon (C) and boron nitride (BN) holey graphyne (HGY) monolayers. Density functional theory (DFT) results reveal that while the C-HGY monolayer shows an appealing direct gap of 1.00 (0.50) eV according to the HSE06(PBE) functional, the BNHGY monolayer is an indirect insulator with large band gaps of 5.58 (4.20) eV. Furthermore, the elastic modulus (ultimate tensile strength) values of the single-layer C- and BN-HGY are predicted to be 127(41) and 105(29) GPa, respectively. The phononic and thermal properties are further investigated using machine learning interatomic potentials (MLIPs). The predicted phonon spectra confirm the dynamical stability of these novel nanoporous lattices. The room temperature lattice thermal conductivity of the considered monolayers is estimated to be very close, around 14.0 ± 1.5 W/mK. At room temperature, the C-HGY and BN-HGY monolayers are predicted to yield an ultrahigh negative thermal expansion coefficient, by more than one order of magnitude larger than that of the graphene. The presented results reveal decent stability, anomalously low elastic modulus to tensile strength ratio, ultrahigh negative thermal expansion coefficients and moderate lattice thermal conductivity of the semiconducting C-HGY and insulating BN-HGY monolayers. Full article
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19 pages, 4705 KiB  
Article
The Effect of Hole Geometry on the Nonlinear Nanomechanics of γ-Graphyne Structures: A Finite Element Analysis
by Stelios K. Georgantzinos, Sotirios G. Siampanis, Nikolaos Rogkas and Vasilios Spitas
Int. J. Mol. Sci. 2023, 24(19), 14524; https://doi.org/10.3390/ijms241914524 - 25 Sep 2023
Cited by 1 | Viewed by 1226
Abstract
Graphyne is a material that has unique mechanical properties, but little is known about how these properties change when the material has holes. In this work, the effect of hole geometry, considering circular, triangle, and rhombus hole configurations, on the mechanical nonlinear response [...] Read more.
Graphyne is a material that has unique mechanical properties, but little is known about how these properties change when the material has holes. In this work, the effect of hole geometry, considering circular, triangle, and rhombus hole configurations, on the mechanical nonlinear response of γ-graphyne structures is studied. Graphyne, graphdiyne, graphyne-3, and graphyne-4 structures are under investigation. An efficient nonlinear finite element analysis (FEA) method is adequately implemented under large deformations for this purpose. The study varied the size and shape of the holes to understand how these changes affect the nanostructure’s mechanical response. The results indicate that the hole geometry significantly impacts the mechanical nonlinear response of γ-graphyne structures. The holes’ size and shape affect the structures’ elastic behavior, deformation, and strength. The findings can be used to optimize the design of γ-graphyne structures for specific mechanical applications. The study highlights the importance of considering the hole geometries in the design and fabrication of these materials. Full article
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18 pages, 14879 KiB  
Article
Computational Studies on Diverse Characterizations of Molecular Descriptors for Graphyne Nanoribbon Structures
by Muhammad Awais Raza, Muhammad Khalid Mahmood, Muhammad Imran, Fairouz Tchier, Daud Ahmad and Muhammad Kashif Masood
Molecules 2023, 28(18), 6597; https://doi.org/10.3390/molecules28186597 - 13 Sep 2023
Viewed by 1433
Abstract
Materials made of graphyne, graphyne oxide, and graphyne quantum dots have drawn a lot of interest due to their potential uses in medicinal nanotechnology. Their remarkable physical, chemical, and mechanical qualities, which make them very desirable for a variety of prospective purposes in [...] Read more.
Materials made of graphyne, graphyne oxide, and graphyne quantum dots have drawn a lot of interest due to their potential uses in medicinal nanotechnology. Their remarkable physical, chemical, and mechanical qualities, which make them very desirable for a variety of prospective purposes in this area, are mostly to blame for this. In the subject of mathematical chemistry, molecular topology deals with the algebraic characterization of molecules. Molecular descriptors can examine a compound’s properties and describe its molecular topology. By evaluating these indices, researchers can predict a molecule’s behavior including its reactivity, solubility, and toxicity. Amidst the captivating realm of carbon allotropes, γ-graphyne has emerged as a mesmerizing tool, with exquisite attention due to its extraordinary electronic, optical, and mechanical attributes. Research into its possible applications across numerous scientific and technological fields has increased due to this motivated attention. The exploration of molecular descriptors for characterizing γ-graphyne is very attractive. As a result, it is crucial to investigate and predict γ-graphyne’s molecular topology in order to comprehend its physicochemical characteristics fully. In this regard, various characterizations of γ-graphyne and zigzag γ-graphyne nanoribbons, by computing and comparing distance-degree-based topological indices, leap Zagreb indices, hyper leap Zagreb indices, leap gourava indices, and hyper leap gourava indices, are investigated. Full article
(This article belongs to the Section Computational and Theoretical Chemistry)
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11 pages, 6355 KiB  
Article
Molecular Simulations of the Gas Diffusion through the Two-Dimensional Graphyne Membrane
by Dongliang Jin, Tao Zhang, Meng Guo, Nanhua Wu and Jing Zhong
Separations 2023, 10(9), 499; https://doi.org/10.3390/separations10090499 - 13 Sep 2023
Viewed by 1984
Abstract
Owing to the unified and tunable pore size, two-dimensional graphyne membranes show excellent performance in the realm of gas transport and separations. The impacts of environmental conditions on the pore size of a porous membrane are ignored in previous studies. Using molecular modeling [...] Read more.
Owing to the unified and tunable pore size, two-dimensional graphyne membranes show excellent performance in the realm of gas transport and separations. The impacts of environmental conditions on the pore size of a porous membrane are ignored in previous studies. Using molecular modeling techniques, we here probe the accessible pore size of the γ-graphyne membrane under various pressure and temperature conditions. First, by assessing the gas permeation through the two-dimensional γ-graphyne membrane at a constant temperature, the accessible pore size of this membrane is shown to be proportional to the driving force—the pressure difference between the two sides of the porous membrane. Such a driving force dependence is found to be well described by a simple asymptotic model. Then, by determining such pressure dependence at two different temperatures, temperature is found to show a weak influence on the accessible pore size. Finally, by considering the binary mixed gases of various mole fractions, the accessible pore size measured using one of the two species is shown to be dependent on its partial pressure difference. These findings for the accessible pore size, which highlight the tunable pore size by altering the driving force, can be expected to provide a practical strategy to rationalize/refine the pore size of the porous membrane for gas transport and separations, especially for two molecules with similar diameters. Full article
(This article belongs to the Section Materials in Separation Science)
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19 pages, 738 KiB  
Article
Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials
by César R. de Oliveira and Vinícius L. Rocha
C 2023, 9(3), 76; https://doi.org/10.3390/c9030076 - 8 Aug 2023
Cited by 1 | Viewed by 1756
Abstract
It is shown that it is possible to adapt the quantum graph model of graphene to some types of nonequilateral graphynes considered in the literature; we also discuss the corresponding nanotubes. The proposed models are, in fact, effective models and are obtained through [...] Read more.
It is shown that it is possible to adapt the quantum graph model of graphene to some types of nonequilateral graphynes considered in the literature; we also discuss the corresponding nanotubes. The proposed models are, in fact, effective models and are obtained through selected boundary conditions and an ad hoc prescription. We analytically recover some results from the literature, in particular, the presence of Dirac cones for α-, β- and (6,6,12)-graphynes; for γ-graphyne, our model presents a band gap (according to the literature), but only for a range of parameters, with a transition at a certain point with quadratic touch and then the presence of Dirac cones. Full article
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13 pages, 3691 KiB  
Article
Theoretical Study of 3d VIII Atom-Decorated γ-Graphyne for Adsorbing and Detecting Heptafluoroisobutyronitrile
by Ziang Zheng, Renchu Zhao, Dachang Chen, Qing Miao, Ke Liu and Beibei Xiao
Chemosensors 2023, 11(7), 411; https://doi.org/10.3390/chemosensors11070411 - 21 Jul 2023
Cited by 11 | Viewed by 1762
Abstract
Recently, Heptafluoroisobutyronitrile (C4F7N) has received widespread attention in replacing one of the most greenhouse-insulating gas, SF6. However, gas leakage is incredibly harmful to the health of operational personnel and the security of industry production, and developing C [...] Read more.
Recently, Heptafluoroisobutyronitrile (C4F7N) has received widespread attention in replacing one of the most greenhouse-insulating gas, SF6. However, gas leakage is incredibly harmful to the health of operational personnel and the security of industry production, and developing C4F7N detection technology is of great necessity. In this work, the adsorption properties, as well as the sensing performance of C4F7N on 3d VIII atom-decorated γ-graphyne (γ-GY), were theoretically discussed. The adsorption structures, adsorption energies, electron transfer, adsorption distance, electron distribution, and electronic properties were compared. The results show that the introduction of Fe and Co atom enhance the chemisorption of C4F7N, and the adsorption of C4F7N brings the maximum electron redistribution of Fe/γ-GY among three TM/γ-GY. Only the adsorption on Fe/γ-GY leads to the vanishing of the magnetic moment and creates a band gap. For three different modifications of γ-GY, the chemical interactions are highly related to the overlapping of transition metal 3d and N 2p orbitals in the density of states. The adsorption on Co/γ-GY causes the maximum change in work function from 5.06 eV to 5.26 eV. In addition, based on the band structure, work function, and desorption properties, the sensing properties of 3d VIII atom-decorated γ-GY were evaluated in order to promote the experimental exploration and development of high-performance C4F7N gas sensors. Full article
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15 pages, 66052 KiB  
Article
Performance Analysis of an α-Graphyne Nano-Field Effect Transistor
by Habibullah Khan, Md. Monirul Islam, Rajnin Imran Roya, Sariha Noor Azad and Mahbub Alam
Micromachines 2023, 14(7), 1385; https://doi.org/10.3390/mi14071385 - 6 Jul 2023
Cited by 1 | Viewed by 2510
Abstract
Graphyne has attractive electronic properties that make it a possible replacement of silicon in FET technology. In FET technology, the goal is to achieve low power dissipation and lower subthreshold swing. In this study, we focused on achieving these goals and studied the [...] Read more.
Graphyne has attractive electronic properties that make it a possible replacement of silicon in FET technology. In FET technology, the goal is to achieve low power dissipation and lower subthreshold swing. In this study, we focused on achieving these goals and studied the electronic properties of α-graphyne nanoribbons. We simulated the transfer and output characteristics of an α-graphyne ballistic nanoribbon FET. We used the tight-binding model with nearest-neighbor approximation to obtain the band structure which gives the same band structure as the one found from the DFT. In order to simulate the I-V characteristics of the transistor we used the non-equilibrium Green’s function (NEGF) formalism. The results show that the modeled FET can provide a high Ion/Ioff ratio and low subthreshold swing. We also studied the effects of defects as defects cannot be avoided in any practical device. The study shows that the Ion/Ioff ratio and subthreshold swing improves as defects are added, but the delay time and dynamic power dissipation worsen. Full article
(This article belongs to the Special Issue Novel Electronics Devices Integrated with 2D Quantum Materials)
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15 pages, 3449 KiB  
Article
Theoretical Investigation of HER and OER Electrocatalysts Based on the 2D R-graphyne Completely Composed of Anti-Aromatic Carbon Rings
by Cuimei Li, Tianya Li, Guangtao Yu and Wei Chen
Molecules 2023, 28(9), 3888; https://doi.org/10.3390/molecules28093888 - 5 May 2023
Cited by 8 | Viewed by 2798
Abstract
Based on the DFT calculations, two-dimensional (2D) R-graphyne has been demonstrated to have high stability and good conductivity, which can be conducive to the relevant electrocatalytic activity of the material. Different from the poor graphene, R-graphyne, which is completely composed of anti-aromatic structural [...] Read more.
Based on the DFT calculations, two-dimensional (2D) R-graphyne has been demonstrated to have high stability and good conductivity, which can be conducive to the relevant electrocatalytic activity of the material. Different from the poor graphene, R-graphyne, which is completely composed of anti-aromatic structural units, can exhibit certain HER catalytic activity. In addition, doping the TM atoms in Group VIIIB can be considered an effective strategy to enhance the HER catalytic activity of R-graphyne. Particularly, Fe@R-graphyne, Os@R-graphyne, Rh@R-graphyne and Ir@R-graphyne can exhibit higher HER catalytic activities due to the formation of more active sites. Usually, the shorter the distance between the TM and C atoms is, the better the HER activity of the C-site is. Furthermore, doping Ni and Rh atoms of Group VIIIB can significantly improve the OER catalytic performance of R-graphyne. It can be found that ΔGO* can be used as a good descriptor for the OER activities of TM@R-graphyne systems. Both Rh@R-graphyne and Ni@R-graphyne systems can exhibit bifunctional electrocatalytic activities for HER/OER. In addition, all the relevant catalytic mechanisms are analyzed in detail. This work not only provides nonprecious and highly efficient HER/OER electrocatalysts, but also provides new ideas for the design of carbon-based electrocatalysts. Full article
(This article belongs to the Section Computational and Theoretical Chemistry)
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11 pages, 5161 KiB  
Article
Facile Synthesis of Hydrogen-Substituted Graphdiyne Powder via Dehalogenative Homocoupling Reaction
by Jiayi Yin, Jizhe Liang, Chunxue Yuan and Wei Zheng
Nanomaterials 2023, 13(6), 1018; https://doi.org/10.3390/nano13061018 - 11 Mar 2023
Cited by 8 | Viewed by 2775
Abstract
Graphdiyne and its analogs are a series of artificial two-dimensional nanomaterials with sp hybridized carbon atoms, which can be viewed as the insertion of two acetylenic units between adjacent aromatic rings, evenly expanded on a flat surface. Although developed in recent years, new [...] Read more.
Graphdiyne and its analogs are a series of artificial two-dimensional nanomaterials with sp hybridized carbon atoms, which can be viewed as the insertion of two acetylenic units between adjacent aromatic rings, evenly expanded on a flat surface. Although developed in recent years, new synthetic strategies for graphdiyne analogs are still required. This work proposed a new method to prepare hydrogen-substituted graphdiyne powder via a dehalogenative homocoupling reaction. The polymerization was unanticipated while the initial goal was to synthesize a γ-graphyne analog via Sonogashira cross-coupling reaction. Compared with previous synthetic strategies, the reaction time was conspicuously shortened and the Pd catalyst was inessential. The powder obtained exhibited a porous structure and high electrocatalytic activity in the hydrogen/oxygen evolution reaction, which has the potential for application in electrochemical catalysis. The reported methodology provides an efficient synthetic strategy for large-scale preparation. Full article
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12 pages, 4183 KiB  
Article
Thermal Stability and Vibrational Properties of the 6,6,12-Graphyne-Based Isolated Molecules and Two-Dimensional Crystal
by Ekaterina S. Dolina, Pavel A. Kulyamin, Anastasiya A. Grekova, Alexey I. Kochaev, Mikhail M. Maslov and Konstantin P. Katin
Materials 2023, 16(5), 1964; https://doi.org/10.3390/ma16051964 - 27 Feb 2023
Cited by 4 | Viewed by 2141
Abstract
We report the geometry, kinetic energy, and some optical properties of the 6,6,12-graphyne-based systems. We obtained the values of their binding energies and structural characteristics such as bond lengths and valence angles. Moreover, using nonorthogonal tight-binding molecular dynamics, we carried out a comparative [...] Read more.
We report the geometry, kinetic energy, and some optical properties of the 6,6,12-graphyne-based systems. We obtained the values of their binding energies and structural characteristics such as bond lengths and valence angles. Moreover, using nonorthogonal tight-binding molecular dynamics, we carried out a comparative analysis of the thermal stability of 6,6,12-graphyne-based isolated fragments (oligomer) and two-dimensional crystals constructed on its basis in a wide temperature range from 2500 to 4000 K. We found the temperature dependence of the lifetime for the finite graphyne-based oligomer as well as for the 6,6,12-graphyne crystal using a numerical experiment. From these temperature dependencies, we obtained the activation energies and frequency factors in the Arrhenius equation that determine the thermal stability of the considered systems. The calculated activation energies are fairly high: 1.64 eV for the 6,6,12-graphyne-based oligomer and 2.79 eV for the crystal. It was confirmed that the thermal stability of the 6,6,12-graphyne crystal concedes only to traditional graphene. At the same time, it is more stable than graphene derivatives such as graphane and graphone. In addition, we present data on the Raman and IR spectra of the 6,6,12-graphyne, which will help distinguish it from the other carbon low-dimensional allotropes in the experiment. Full article
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31 pages, 9539 KiB  
Article
Neighbourhood Sum Degree-Based Indices and Entropy Measures for Certain Family of Graphene Molecules
by Jun Yang, Julietraja Konsalraj and Arul Amirtha Raja S.
Molecules 2023, 28(1), 168; https://doi.org/10.3390/molecules28010168 - 25 Dec 2022
Cited by 20 | Viewed by 2859
Abstract
A topological index (TI) is a real number that defines the relationship between a chemical structure and its properties and remains invariant under graph isomorphism. TIs defined for chemical structures are capable of predicting physical properties, chemical reactivity and biological activity. Several kinds [...] Read more.
A topological index (TI) is a real number that defines the relationship between a chemical structure and its properties and remains invariant under graph isomorphism. TIs defined for chemical structures are capable of predicting physical properties, chemical reactivity and biological activity. Several kinds of TIs have been defined and studied for different molecular structures. Graphene is the thinnest material known to man and is also extremely strong while being a good conductor of heat and electricity. With such unique features, graphene and its derivatives have found commercial uses and have also fascinated theoretical chemists. In this article, the neighbourhood sum degree-based M-polynomial and entropy measures have been computed for graphene, graphyne and graphdiyne structures. The proper analytical expressions for these indices are derived. The obtained results will enable theoretical chemists to study these exciting structures further from a structural perspective. Full article
(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)
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